Feedback from supercritical disk accretion flows; Two-dimensional radiation-hydrodynamic simulations of stable and unstable disks with radiatively driven outflows

The supercritical disk accretion flow with radiatively driven outflows is studied based on two-dimensional radiation-hydrodynamic simulations for a wide range of the mass input rate, $\dot{M}_{\rm input}$, which is the mass supplied from the outer region to the disk per unit time. The $\alpha$-prescription is adopted for the viscosity. We employ $\alpha=0.5$, as well as $\alpha=0.1$ for $\dot{M}_{\rm input}\ge 3\times 10^2L_{\rm E}/c^2$ and only $\alpha=0.5$ for $\dot{M}_{\rm input}\le 10^2L_{\rm E}/c^2$, where $L_{\rm E}$ is the Eddington luminosity and $c$ is the speed of light. The quasi-steady disk and radiately driven outflows form in the case in which the mass input rate highly exceeds the critical rate, $\dot{M}_{\rm input}>3\times 10^2 L_{\rm E}/c^2$. Then, the disk luminosity as well as the kinetic energy output rate by the outflow exceeds the Eddington luminosity. The moderately supercritical disk, $\dot{M}_{\rm input}\sim 10-10^2 L_{\rm E}/c^2$, exhibits limit-cycle oscillations. The disk luminosity goes up and down across the Eddington luminosity, and the radiatively driven outflows intermittently appear. The time averaged mass, momentum, and kinetic energy output rates by the outflow as well as the disk luminosity increase with increase of the mass input rate, $\propto \dot{M}_{\rm input}^{0.7-1.0}$ for $\alpha=0.5$ and $\propto \dot{M}_{\rm input}^{0.4-0.6}$ for $\alpha=0.1$. Our numerical simulations show that the radiatively driven outflow model for the correlation between black hole mass and bulge velocity dispersion proposed by \citeauthor{SR98} and \citeauthor{King03} is successful if $\dot{M}_{\rm input}c^2/L_{\rm E} \sim$ a few 10 ($\alpha=0.5$) or $\gsim$ a few ($\alpha=0.1$).